The field of hydrocarbon production is directed to retrieving hydrocarbons that are trapped in subsurface reservoirs. These hydrocarbons can be recovered by drilling wells into the reservoirs such that hydrocarbons are able to flow from the reservoirs into the wells and up to the surface. The geology of a reservoir has a large impact on the production rate at which hydrocarbons are able to flow into a well. A large amount of effort has therefore, been dedicated to developing reservoir characterization and simulation techniques to better predict how fluid will flow within a reservoir.
Highly complex geological subsurface reservoirs, such as reservoirs having a network of fractures, present unique and specialized challenges with regards to simulating fluid flow. A fractured reservoir is a reservoir in which fractures enhance the permeability field, thereby significantly affecting well productivity and recovery efficiency. Fractures can be described as open cracks or voids embedded within the rock matrix, and can either be naturally occurring or artificially generated from a wellbore. Natural fractures typically occur in sets of parallel fractures that can range several orders of magnitude in size. The length distribution within a fracture set is characteristically non-linear, with many short fractures and a diminishing number of large fractures. The range of fracture apertures is distributed in a similar manner. Furthermore, several fracture sets can coexist in a rock forming connected networks of significant extent and complexity. Fracture networks can play an important role in allowing fluids to flow through the reservoir to reach a well. For example, a well that intersects a fracture network often produces fluid at a rate that greatly exceeds the rate of flow within the rock matrix, as the fracture network typically has a much greater capability to transport fluids. Accordingly, a network of multiple intersecting fractures often forms the basis for flow in fractured reservoirs.
Mathematical formulations describing flow in naturally fractured porous media are typically governed by highly heterogeneous anisotropic tensorial coefficients (hydraulic conductivity) at different scales. In addition to the complex geometries of fracture networks, the high contrast in the physical properties and length scales, compared to those of the reservoir matrix, results in very expensive fine-scale simulations. Therefore, many studies have been dedicated to reduce the physical and numerical complexities arising in simulation of flow in fractured reservoirs. As a result various modeling approaches and numerical strategies suitable for different types of fractures have been proposed.
Among the proposed approaches, a dual porosity model approach has been proposed for naturally fractured porous media containing many small fractures. This method introduces effective coefficients for (n−1) dimensional (D) fractures by mapping them into a continuum domain (nD). This upscaling based strategy results in reasonably efficient simulations with the cost of additional assumptions. However, this method is generally only appropriate for problems with small scale fractures. For problems with long scale fractures, this approach typically fails to provide good solutions as no general upscaling strategy is possible in this approach.
A discrete fracture modeling approach has also been devised to obtain more accurate simulations. In this approach, the geometry and locations of fractures are honored accurately by applying complex unstructured gridding techniques. In particular, the grid is generated with the constraints that the fracture elements are located at the matrix cell interfaces and such that the matrix cells around the fractures are constructed small enough to capture the correct fracture geometries. The latter constraint often results in very small cells, especially near intersections. Such small cells can lead to big linear systems and can also impose time step restrictions for multiphase transport simulations. This approach, therefore, has limited applicability for realistic scenarios due to the complex conforming grids. Moreover, this approach is typically not suited for dynamic fracture network problems, such as in simulations of enhanced geothermal systems, where the grid is frequently updated due to generations of new fractures.
Another proposed approach utilizes a hierarchical fracture network model. In this method, small scale fractures are homogenized and treated as a continuous matrix with effective coefficients. Large-scale fractures are explicitly represented by a coupled discrete fracture model. In particular, simple structured nD and (n−1)D grids are independently generated for matrix and fractures, respectively. In this method, the fracture lines can be located independent of the reservoir matrix grid and therefore, no additional complexity is introduced into the reservoir matrix grid.
The aforementioned methods, including treating fractures explicitly by complex grids (discrete fracture network modeling), by source terms (hierarchical approach), or by a combination of both (hybrid methods), often result in large systems that are typically expensive to solve when applied to realistic problems. A new computationally efficient method for simulations of realistic multiphase flow in fractured heterogeneous porous media is therefore needed.